Following a verb, both 一下 ((yí xià, lit. “once”) and(一)点儿 ({yì} diǎnr “a bit”) can soften the tone in a question or an imperative sentence, therefore making it more polite. When used in this way, 一下(yí xià) modifies the verb, while(一)点儿 ({yì} diǎnr) modifies the object.
For example:
nǐ kàn yí xià , zhè shì shuí de zhào piàn ?
你看一下,这是谁的照片? Take a look. Whose photo is this?
nǐ xiǎnɡ chī diǎnr shén me ?
你想吃点儿什么? What would you like to eat?
nǐ jìn lái yí xià 。
你进来一下。Come in for a minute.
wǒ men hē yì diǎnr chá bɑ 。
我们喝一点儿茶吧。 Have a little tea.
qǐnɡ nǐ kāi yí xià mén 。
请你开一下门。 Please open the door.